# A first-principles study of the vibrational properties of crystalline tetracene under pressure

TL;DR: The results suggest that the experimentally reported improvement of the photocurrent under pressure may be ascribed to an increase in intermolecular interactions as also the dielectric tensor.

Abstract: We present a comprehensive study of the hydrostatic pressure dependence of the vibrational properties of tetracene using periodic density-functional theory (DFT) within the local density approximation (LDA). Despite the lack of van der Waals dispersion forces in LDA we find good agreement with experiment and are able to assess the suitability of this approach for simulating conjugated organic molecular crystals. Starting from the reported x-ray structure at ambient pressure and low temperature, optimized structures at ambient pressure and under 280 MPa hydrostatic pressure were obtained and the vibrational properties calculated by the linear response method. We report the complete phonon dispersion relation for tetracene crystal and the Raman and infrared spectra at the centre of the Brillouin zone. The intermolecular modes with low frequencies exhibit high sensitivity to pressure and we report mode-specific Gruneisen parameters as well as an overall Gruneisen parameter [Formula: see text]. Our results suggest that the experimentally reported improvement of the photocurrent under pressure may be ascribed to an increase in intermolecular interactions as also the dielectric tensor.

## Summary (3 min read)

### 1. Introduction

- Organic semiconductors have great potential as active materials in optoelectronic devices.
- A recent DFT study performed on tetracene and other molecular crystals, and containing a correction for the vdW interactions, correctly predicts the structural, electronic and optical properties of the crystals [19, 20].
- So for this study the authors return to the local density approximation (LDA).
- Though it lacks a physically correct description of vdW dispersion forces, this is compensated by a tendency to overbind which usually gives fairly good predictions of equilibrium geometry in weakly-bonded molecular crystals.
- However this has not yet been examined in detail.

### 2. Method and Computational Details

- The authors calculations used the CASTEP code [27] which implements the plane-wavepseudopotential formulation of DFT together with density-functional perturbation theory (DFPT).
- The two structures converged to the same minimum total energy within 6 meV per unit cell and to equivalent unit cell parameters, in agreement with reference [33].
- Calculations were performed on a unit cell of this tetracene crystal containing two symmetrically inequivalent molecules so that the unit cell contains a total of 36 carbon and 24 hydrogen atoms.
- The coarse grid contains 14 irreducible q-points.

### 3.1 Optimisation of Tetracene Structure at Ambient and 280 MPa Pressures

- Table 1 presents DFT-LDA results for unconstrained optimisation of the LT structure at ambient pressure conditions together with the experimentally reported LT data [31].
- In accordance with the well-known tendency of the LDA to overbind the atoms [40, 41], the volume of the DFT-LDA optimised structure at ambient pressure was smaller by ~11% than the experimentally measured volume, despite the lack of vdW forces.
- Upon optimisation, the lengths of all the lattice vectors decreased, with a maximum reduction in b of ~5%, but the cell angles did not change appreciably.
- The overlap between the molecular wavefunctions in the ab plane increases.
- Upon the application of a small amount of pressure, the interlayer distance Z is almost unchanged, but there is a slight increase in the angle between the planes of the adjacent molecules from 150.1° to 150.6°.

### 3.2. Phonon Dispersion Curves

- Figure 2 displays the phonon dispersion curves 𝜔(𝑞) computed for the two optimised structures of tetracene along a path that includes the high symmetry q-points and a few others in the triclinic unit cell.
- The intermolecular and low-lying intramolecular modes shown in Figure 2 (a,b) are highly dispersive, while the higherfrequency intramolecular modes shown in Figure 2 (c,d) exhibit much less dispersion.
- Figure 4 shows schematic illustrations of the atomic and molecular displacement associated with some of the DFT-LDA calculated phonons below 300 cm -1 .
- Further detailed information on the displacement of atoms corresponding to each of the 180 modes is available in the supplementary information.
- In general, modes are shifted to higher frequencies when tetracene is compressed, indicating that the crystal becomes stiffer.

### 3.3 Grüneisen Parameters

- Grüneisen parameters for each phonon mode are defined by the dependence of the phonon frequencies on the crystal volume.
- The overall crystal Grüneisen parameter is evaluated by averaging the individual mode-Grüneisen parameters, weighted by their specific heat contributions (see supplementary information).
- The overall crystal Grüneisen parameter of tetracene computed by DFT-LDA is 2.82, which is ‘qualitatively’ similar to that measured and calculated as 3.6 and 3.46, respectively for naphthalene [50].
- Figure 6(b) shows the modeGrüneisen parameters at the zone-centre for the modes below 600 cm -1 .
- It may be seen that modes with frequency below 155 cm -1 are the most pressure sensitive, with Grüneisen parameters around 3, decreasing to less than 1 at higher frequencies.

### 3.4 Pressure Dependence of Raman and Infrared Spectra

- The modes of the DFT-LDA-calculated phonons were assigned using symmetry group analysis for tetracene, , which predicts a total of 90 modes for each of the symmetry modes Au and Ag respectively.
- The frequencies of the low-lying Raman-active modes at ambient pressure conditions calculated using DFT-LDA plotted against the experimentally measured frequencies in Ref.[25] show excellent agreement, as indicated by the slope of (1.04±0.02) and correlation coefficient of 0.998 (see supplementary information).
- A small scaling error – in this case 1.04 is typical and expected of the comparison between DFT and experimental frequencies.
- This upshift is non-uniform, 1P 1iC showing some variance among the mode Grüneisen parameters.
- This work additionally predicts several bands in the intermolecular low frequency region below 160 cm -1 .

### 3.5 Pressure Dependence of Dielectric Constant

- The propagation of radiation through the crystal subject to a low-frequency (IR and lower) external electric field is described by the static dielectric tensor (𝜀0) whilst the optical tensor (𝜀∞) describes the interaction of the crystal with a high-frequency electric field.
- Because of the triclinic symmetry of the tetracene crystal, both the static and optical dielectric tensors are anisotropic with three distinct diagonal components 𝜀𝑥𝑥 , 𝜀𝑦𝑦 and 𝜀𝑧𝑧 .
- The DFT-LDA calculated optical dielectric constant at ambient pressure is higher than the experimentally reported values due to the underestimation of the band gap, which is inversely proportional to 𝜀(𝜔) [57, 58].
- This shows that 𝜀(𝜔) is sensitive to the change that occurs along the b direction within the ab herringbone plane in the unit cell rather than along the c direction of the stacking layers.
- Furthermore, the increase in the transfer integral leads to an increase in the mobility of charge carriers in accord with the experimental observation [21].

### 4. Conclusions

- The applicability of DFT-LDA to probe the pressure dependence of structural and vibrational properties of organic molecular crystals has been assessed through the calculation of tetracene properties.
- In spite of the lack of account of vdW dispersion forces and the tendency of DFT-LDA to overbind atoms, resulting in smaller calculated volumes than found in experiment, there is good agreement for the vibrational properties and associated Raman and infrared spectra between theory and experiment.
- For the first time, the complete set of phonon dispersion relations have been presented for tetracene enabling computation of the Grüneisen parameter.
- As indicated by the mode-specific Grüneisen parameters, the intermolecular modes were more sensitive to the applied pressure than the intramolecular modes as expected.
- The DFT-LDA results also reveal that application of hydrostatic pressure increases the dielectric tensors anisotropically with a maximum change exhibited along the b axis.

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...Initially, the two available X-ray crystal structures of tetracene labelled TETCEN [30], recorded at room temperature (RT), and TETCEN01 [31], recorded at a low temperature (LT) of 175 K, available from the Cambridge Structural Database (CSD) [32] were geometry-optimised....

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...available from the Cambridge Structural Database (CSD) [32] were geometry-optimised....

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